Shultz, T. R., & Elman, J. L.
(1994). Analyzing cross connected networks. In J. D. Cowan, G. Tesauro, &
J. Alspector (Eds.), *Advances in Neural Information Processing
Systems 6* (pp. 1117-1124). San Francisco, CA: Morgan Kaufmannn.

The non-linear complexities of neural networks make network
solutions difficult to understand. Sanger's *contribution
analysis* is here extended to the analysis of networks automatically
generated by the cascade-correlation learning algorithm. Because such networks
have cross connections that supersede hidden layers, standard analyses of
hidden unit activation patterns are insufficient. A *contribution* is defined as the product of an output weight and the
associated activation on the sending unit, whether that sending unit is an
input or a hidden unit, multiplied by the sign of the output target for the
current input pattern. Intercorrelations among contributions, as gleaned from
the matrix of contributions x input patterns, can be subjected to principal
components analysis (PCA) to extract the main features of variation in the
contributions. Such an analysis is applied to three problems, continuous XOR,
arithmetic comparison, and distinguishing between two interlocking spirals. In
all three cases, this technique yields useful insights into network solutions
that are consistent across several networks.

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